Kansas is mostly a gigantic farm and there’s farm roads every mile or so. Laying out roads along section (square mile, 640 acres) or quarter section (160 acre) boundaries is probably how Kansas developed its road network. 36 sections make up a township, 6 sections by 6 sections. Most (?) land between California and the Mississippi River is surveyed like this, probably excluding Texas since that was a country and originally held by Spain/Mexico.

The Wikipedia article for section (survey) has an aerial photo of Kansas in it, naturally: https://en.wikipedia.org/wiki/Section_(United_States_land_su...